Acoustic wave device

ABSTRACT

In an acoustic wave device, in a rotated Y-cut crystal substrate to which a rotational angle based on a particular Euler angle is added, a vibration mode located farther in a low phase velocity area than the principal vibration has an electromechanical coupling coefficient K2 lower than that of the principal vibration, and the primary and secondary temperature coefficients of the principal vibration are approximately zero. The acoustic wave device includes a crystal substrate cut from a quartz crystal boule cut by a rotational angle specified by a right-handed Euler angle (ϕ, θ, Ψ), and at least one comb-shape excitation electrode to excite the crystal substrate to make a plate waves. The crystal substrate is made by cutting the quartz crystal boule such that the rotational angle is within ranges of ϕ=0±2°, θ=17.5° to 19.5°, and Ψ=0±2°.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is based on and claims benefit of JapanesePatent Application No. 2020-138146 filed on Aug. 18, 2020, thedisclosure of which is incorporated herein by reference in its entirety.

TECHNICAL FILED

The present application relates to acoustic wave devices used inhigh-frequency oscillation sources in instruments such as computers andcommunications instruments.

DISCUSSION OF THE BACKGROUND

The statements in this section merely provide background informationrelated to the present disclosure and do not necessarily constituteprior art.

Japanese laid-open application publication No. JP57-68925A discloses apiezoelectric device that uses an elastic wave mode occurring in arotated Y-cut crystal substrate. The piezoelectric device has such astructure that a comb-shaped excitation electrode is formed on the frontsurface of a crystal substrate and that a thin film used for frequencyadjustment purposes is formed on the back surface of the crystalsubstrate. The crystal substrate is made by cutting a quartz crystalboule by defining a predetermined rotational angle specified by Eulerangle.

Japanese laid-open application publication No. JP 2003-258596A andJapanese Patent No. JP 4465464B disclose resonators for making elasticwaves oscillate. In those disclosed resonators, the crystal substrate ismade by cutting a quartz crystal boule by defining a predeterminedrotational angle specified by Euler angle. And the cutting angles of thecrystal substrate are specified by two-axis rotational angles. Theresonators disclosed in these patent documents have such a structurethat a comb-shape excitation electrode is provided on a surface of thepiezoelectric substrate, and that in this structure, no thin film andassociated elements for adjusting frequency are provided on the backsurface of the crystal substrate. The resonator disclosed in JapanesePatent No. JP 4465464B has such a frequency temperature characteristicthat draws a cubic curve having an inflection point in the vicinity of25° C.

Japanese Patent No. JP 4306668B discloses a high-frequency resonatorconfigured by using a rotated Y-cut crystal substrate specified by Eulerangle. This resonator has such a structure that a comb-shape excitationelectrode is provided on a surface of the piezoelectric substrate, andthat in this structure, no thin film and associated elements foradjusting frequency are provided on the back surface of the crystalsubstrate.

Japanese Patent No. JP 5563378B discloses an acoustic wave device thatincludes a crystal substrate cut by a predetermined Euler angle. In theacoustic wave device, the thickness of the crystal substrate and thethickness of an electrode film formed on the crystal substrate arespecified.

SUMMARY

An acoustic wave device disclosed in the present application includes: acrystal substrate cut from a quartz crystal boule havingthree-dimensional crystal orientations defined by an X axis, a Y axis,and a Z axis, the quartz crystal boule being cut on the Y axis and the Zaxis while being rotated about the X axis, the quartz crystal boulebeing cut by a rotational angle specified by a right-handed Euler angle(ϕ, θ, Ψ); and at least one comb-shape excitation electrode configuredto excite the crystal substrate to make plate waves. The crystalsubstrate is made by cutting the quartz crystal boule such that therotational angle is within ranges of ϕ=0±2°, θ=17.5° to 19.5°, andΨ=0±2°. A plate wave, among the plate waves, having a phase velocity ina range of from 3500 to 4000 m/s, is selected as a vibration mode of thecrystal substrate. When H represents a substrate-thickness of thecrystal substrate and λ represents a wavelength of the plate waves, anormalized plate thickness H/λ is in a range of 1.5<H/λ<2.0.

As used herein, the normalized plate thickness H/λ is obtained bydividing the thickness H (unit: m) of the crystal substrate by thewavelength λ (unit: m), and is a definition used to specify the Hdimension irrespective of designed frequency (=λ). In the followingdescription, the normalized plate thickness will be denoted asnormalized plate thickness H/λ. The same applies in normalizedexcitation-electrode film thickness Hs/λ and normalized back-surfaceelectrode film thickness Hb/λ, which will be described later.

Technical Problem

Currently, mainly AT-cut crystal resonators are widely used asoscillation sources equipped in various kinds of electronic devices,especially for reference signals for wireless applications. Inhigh-frequency applications, signals are used by being multiplied usinga PLL into a predetermined frequency. Also, in some applications wherethere is a need for a signal with minimized noise at high frequency, asurface acoustic wave device, which uses a surface acoustic wave, isused as a direct oscillation source.

Crystal resonators treated with AT-cutting provide their frequencycharacteristics over a stable and wide range of temperature, and assuch, are used as oscillation sources in various kinds of electronicdevices. In applications where such crystal resonators are used ashigh-frequency oscillation sources, high-precision processing techniquesare required, such as decreasing the degree of thinness and increasingthe degree of flatness.

In contrast, surface acoustic waves use a longitudinal wave or a lateralwave occurring on the outer layer surface of a piezoelectric (crystal)substrate, and have such a characteristic that their frequencies areproportional to phase velocity and inversely proportional to wavelength.A surface acoustic wave device, which uses such surface acoustic waves,includes an excitation electrode made up of a plurality of electrodefingers arranged in a comb shape on a surface of a crystal substratethat is formed by being cut at a predetermined cutting angle. Byadjusting the thickness of the excitation electrode and/or the pitchbetween each electrode finger, a predetermined oscillation frequency isobtained.

While the above-described AT-cut crystal resonator is highly accurate inoscillation frequency, the inventor has recognized, jitter is caused tooccur by factors such as phase noise and signal time variation orfluctuation at the time when a signal is multiplied to a predeterminedfrequency. In contrast, surface acoustic wave devices have no phasenoise and jitter problems because surface acoustic wave devices arecapable of directly oscillating high-frequency signals. However, theinventor has recognized that there is room for improvement in accuracyin oscillation frequency as compared with AT cut crystal resonators. Theinventor has further recognized that in resonators such that cuttingangles of crystal substrates are specified by two-axis rotationalangles, there is room for improvement in ease of production and/orvariation in frequency temperature characteristic.

In contrast, in acoustic wave devices using plate waves, it is knownthat an vibration wave (plate wave) occurring in an acoustic wave deviceis in such a vibration mode that a lateral wave and a longitudinal waveare connected, and that there are a plurality of vibration modes eachcorresponding to a different degree of combination of the lateral waveand the longitudinal wave. In these-vibration modes using plate waves,as opposed to conventional Rayleigh waves, there may be other-vibrationmodes than a vibration mode intended to be used for an acoustic wavedevice (this vibration mode will be hereinafter referred to as principalvibration). Specifically, there may be vibration modes different inphase velocity (these vibration modes will be hereinafter referred tounnecessary vibrations). When an electrical signal of unnecessaryvibration is converted into a mechanical vibration at a conversionefficiency (this conversion efficiency will be hereinafter referred toas electromechanical coupling coefficient K²), and when the principalvibration and the reflection coefficient have the same sign, then theremay be such a case, at the time when an acoustic wave device isestablished, that the unnecessary vibration has a figure of merit of twoor more and an equivalent series resistance R1 lower than the equivalentseries resistance R1 of the principal vibration. It is to be noted thatthe term “figure of merit” is a quotient obtained by dividing Q value ofan acoustic wave device by capacity ratio γ, and indicates a vibrationstrength of a mechanical acoustic wave device as seen from an electricterminal. This has caused an abnormal oscillation at the time of makingan oscillation at an oscillation circuit. Also, in Colpitts oscillationcircuits, which are commonly used, an abnormal oscillation may possiblyoccur when the above-described unnecessary vibration is located fartherin a low frequency area than the principal vibration.

In an acoustic wave device that includes a crystal substrate cut by apredetermined Euler angle and the thickness of the crystal substrate andthe thickness of an electrode film formed on the crystal substrate arespecified, primary and secondary temperature coefficients can be madeclose to a value of zero by adjusting the Euler angle specified and/orthe thickness of the crystal substrate. However, the inventor hasrecognized that this range of Euler angle has a limitation in makingtertiary temperature coefficient close to a value of zero. In suchacoustic wave device, an unnecessary vibration of a largeelectromechanical coupling coefficient K² exists farther in the lowfrequency area than the principal vibration. Under the circumstances, inthe Colpitts oscillation circuit, an oscillation is made in a vibrationmode located farther in the low frequency area than the principalvibration.

In light of the considerations above, it is an object of the presentapplication to provide an acoustic wave device that ensures that atertiary temperature coefficient closer to a value of zero is obtained.In the acoustic wave device, in a rotated Y-cut crystal substrate towhich a rotational angle based on a particular Euler angle is added, avibration mode located farther in a low phase velocity area than theprincipal vibration has an electromechanical coupling coefficient K²lower than that of the principal vibration; and the primary andsecondary temperature coefficients of the principal vibration are madevalues of approximately zero.

It is also an object of the present application to provide an acousticwave device that: is capable of directly oscillating a high frequency;is superior to AT-cut resonators in oscillation frequency accuracy overa wide range of temperature; and eliminates or minimizes an abnormaloscillation caused by an unnecessary vibration.

Advantageous Effects of Invention

The acoustic wave device disclosed in the present application includes acrystal substrate cut by a conventionally unspecified rotational angleθ, namely, a right-handed Euler angle (ϕ=0±2°, θ=17.5° to 19.5°,Ψ=0±2°). With this crystal substrate by the above-described Euler angle,such a plate wave is selected that the phase velocity is set in therange of from 3500 to 4000 m/s and that the normalized plate thicknessH/λ is in the range of 1.5<H/λ<2.0. By selecting such plate wave,primary temperature coefficient α, secondary temperature coefficient β,and tertiary temperature coefficient γ were Taylor-expanded at 25° C.were made close to values of zero. The following is a Taylor expansionformula indicating a relationship between frequency variation Δf/f andα, β, and γ.Δf/f=α(t−t ₀)+β(t−t ₀)²+γ(t−t ₀)³t₀: Reference temperature

This configuration ensures that the oscillation frequency accuracyincreases over a wide range as compared with conventional acoustic wavedevices and AT-cut resonators, and that high-frequency oscillations areobtained at basic wave. Further with the above configuration, anacoustic wave device having an excellent frequency characteristic, withminimized phase noise and jitter, was obtained. Also, the aboveconfiguration ensures that electromechanical coupling coefficients K² ofall unnecessary vibrations having phase velocity V lower than that of aprincipal vibration are significantly smaller than the electromechanicalcoupling coefficient K² of the principal vibration. This ensures thatthe oscillation frequency accuracy increases over a wide range ascompared with conventional elastic wave resonators and AT-cutresonators, and that abnormal oscillations caused by unnecessaryvibrations are eliminated or minimized.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the present disclosure and many of theattendant advantages thereof will be readily obtained as the samebecomes better understood by reference to the following detaileddescription when considered in connection with the accompanyingdrawings, wherein

FIG. 1 is a perspective view of an exterior of an acoustic wave deviceaccording to an embodiment of the present application.

FIG. 2 shows a right-handed Euler angle coordinate system illustratingcutting angles of the acoustic wave device illustrated in FIG. 1.

FIG. 3 is a graph showing a dispersion of phase velocity Vin vibrationmodes of a plurality of plate waves occurring in the acoustic wavedevice illustrated in FIG. 1.

FIG. 4 is a graph of, obtained by calculation, normalized platethicknesses H/λ in relation to rotational angle θ and primarytemperature coefficient α.

FIG. 5 is a graph of, obtained by calculation, normalized platethicknesses H/λ in relation to rotational angle θ and secondarytemperature coefficient β.

FIG. 6 is a graph of, obtained by calculation, normalized platethicknesses H/λ in relation to rotational angle θ and tertiarytemperature coefficient γ.

FIG. 7 is a graph of, obtained by calculation, normalizedexcitation-electrode film thicknesses Hs/λ in relation to normalizedplate thickness H/λ and primary temperature coefficient α.

FIG. 8 is a graph of, obtained by calculation, normalizedexcitation-electrode film thicknesses Hs/λ in relation to normalizedplate thickness H/λ and secondary temperature coefficient β.

FIG. 9 is a graph of, obtained by calculation, normalizedexcitation-electrode film thicknesses Hs/λ in relation to normalizedplate thickness H/λ and tertiary temperature coefficient γ.

FIG. 10 is a graph showing a relationship between phase velocity V andadmittance Y.

FIG. 11 is a table listing theoretical values and experimental values ofthe phase velocity V corresponding to respective vibration modes.

FIG. 12 is a graph of, obtained by calculation and experimentation,rotational angles θ in relation to normalized plate thickness H/λ andprimary temperature coefficient α.

FIG. 13 is a graph of, obtained by calculation and experimentation,rotational angles θ in relation to normalized plate thickness H/λ andsecondary temperature coefficient β.

FIG. 14 is a graph of, obtained by calculation and experimentation,rotational angles θ in relation to normalized plate thickness H/λ andtertiary temperature coefficient γ.

FIG. 15 is a graph showing a comparison between a theoretical value andan experimental value of each normalized excitation-electrode filmthickness Hs/λ in relation to normalized plate thickness H/λ and primarytemperature coefficient α.

FIG. 16 is a graph showing a comparison between a theoretical value andan experimental value of each normalized excitation-electrode filmthickness Hs/λ in relation to normalized plate thickness H/λ andsecondary temperature coefficient β.

FIG. 17 is a graph showing a comparison between a theoretical value andan experimental value of each normalized excitation-electrode filmthickness Hs/λ in relation to normalized plate thickness H/λ andtertiary temperature coefficient γ.

FIG. 18 is a graph showing measured data of one example of combinationsin which α, β=0.

FIGS. 19A and 19B are perspective views of exteriors of acoustic wavedevices according to other embodiments.

DETAILED DESCRIPTION OF EMBODIMENTS

Embodiments of the subject matter now will be described in furtherdetail hereinafter with reference to the attached figures. In thefigures, identical or corresponding constituents are identified usingthe same reference numerals, and redundant description is omitted. Also,the figures are not necessarily to scale, as the size of some of thestructures or portions of the figures may be exaggerated relative toother structures or portions for illustrative purposes. Further, some ofthe figures are schematically illustrated to facilitate understanding ofthe structures represented therein.

While the specification and drawings detail certain example embodimentsof the subject matter, the subject matter may, however, be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein. Rather, these example embodiments areprovided so that this disclosure will be thorough and complete, and willfully convey the scope of the subject matter to those skilled in theart.

As illustrated in FIG. 1, an acoustic wave device 11 according to thisembodiment includes: a crystal substrate 12, which has a thin planarshape; an excitation electrode 13, which is formed on a front surface 12a of the crystal substrate 12; and a back-surface electrode 14, which isformed on a back surface 12 b of the crystal substrate 12.

The crystal substrate 12 is cut from a quartz crystal boule havingthree-dimensional crystal orientations defined by an X axis, a Y axis,and a Z axis; specifically, the quartz crystal boule is cut on the Yaxis and the Z axis while being rotated about the X axis. The Y axisresulting from the rotation will be referred to as Y′ axis, and the Zaxis resulting from the rotation will be referred to as Z′ axis.

The crystal substrate 12 is cut by a right-handed Euler angle (ϕ=0±2°,θ=17.5° to 19.5°, Ψ=0±2°), and thus is formed into a predeterminedthickness. Also, ϕ and Ψ differential values of α, β, and γ where φ orΨ=0 with respect to a predetermined rotational angle θ from a state ofcrystal symmetry of the crystal substrate are values of zero. Therefore,insofar as ϕ=0±2° and Ψ=0±2°, any change in frequency temperaturecharacteristic is significantly small. A tolerance range of the Eulerangle is ±2.0° because in this range there is no or minimal influence onfrequency temperature characteristic, as recited in Japanese laid-openapplication publication No. JP2003-258596A.

The excitation electrode 13 is made up of a pair of comb-shapeexcitation electrodes 15, 16. The comb-shape excitation electrodes 15,16 include: base electrodes 15 a, 16 a, which are parallel to each otherand extend along a longitudinal direction of the crystal substrate 12;and a plurality of electrode fingers 15 b, 16 b, which extend from sidesurfaces of the respective base electrodes 15 a, 16 a toward the facinglongitudinal directions. Thus, the excitation electrode 13 is arrangedsuch that the electrode fingers 15 b, which extend from the one baseelectrode 15 a, and the electrode fingers 16 b, which extend from theother base electrode 16 a, are in a mutually non-contact state. Thedistance (pitch) between the electrode finger 15 b and the electrodefinger 16 b is set based on the wavelength λ of the plate wave to beexcited. Also, the pitch is approximately λ/2, relative to thewavelength λ. By applying voltage to the excitation electrode 13 suchthat the comb-shape excitation electrodes 15, 16 are different inpolarity, an alternating electric field occurs between adjacentelectrode fingers, thereby exciting a plate wave in the crystalsubstrate 12.

By rotated Y-cutting of the crystal substrate 12, its plate thickness His made into a thickness approximately identical to the wavelength λ ofthe plate wave to be excited. The plate thickness H is adjusted suchthat the principal vibration satisfies a predetermined frequencytemperature characteristic based on a relationship between the thicknessof the excitation electrode 13 and the thickness of the back-surfaceelectrode 14. At the same time, an electromechanical couplingcoefficient K² of an unnecessary vibration located farther in the lowphase velocity area than the principal vibration is set to be smallerthan the electromechanical coupling coefficient of the principalvibration.

As illustrated in FIG. 1, the excitation electrode 13 is providedapproximately at the center of the front surface 12 a of the crystalsubstrate 12, and is a metal film mainly formed of gold (Au) or aluminum(Al). The metal film is formed into a predetermined thickness.Reflectors (not illustrated) may be provided on both sides of theexcitation electrode 13 in its longitudinal direction, so that theexcitation electrode 13 is provided between the reflectors. By providingthe reflectors, the plate wave excited at the excitation electrode 13 isconfined in the space between the reflectors provided on both sides,thereby providing a larger amount of resonance.

The back-surface electrode 14 is formed on the back surface 12 b of thecrystal substrate 12, which is opposite to the excitation electrode 13.The back-surface electrode 14 is formed on the back surface 12 b of thecrystal substrate 12 by making a film that is made of a metal materialsuch as Au or a dielectric material and that has a predeterminedthickness. The metal material may be other than Au such as Al, Ta, andCu, and the dielectric material may be SiO₂, ZnO, or Ta₂O₅. By changingthe thickness of the back-surface electrode 14, which is made of theabove-described material, the oscillation frequency is finely adjusted,and by using the relationship between the plate thickness H and thethickness of the excitation electrode 13, the tertiary temperaturecharacteristic is maintained in the principal vibration.

FIG. 2 shows a right-handed Euler angle coordinate system (φ, θ, Ψ). Inthe figure, φ denotes a rotational angle about the Z axis; θ denotes arotational angle about X′ axis (an angle obtained by rotating the X axisabout the Z axis by φ); and Ψ denotes a rotational angle about Z″ axis(an angle obtained by rotating Z axis about the X′ axis by θ). Also, thecrystal substrate described by Euler angle (ϕ=0°, θ=0°, Ψ=0°) is arotated Z-cut substrate whose main surface is perpendicular to the Zaxis (optical axis) of the quartz crystal boule. In the followingdescription, various kinds of analysis associated with the acoustic wavedevice 11 will be described by referring to this coordinate system. FIG.3 shows dispersion curves of plate waves propagating in the crystalsubstrate 12, which is made by cutting by the Euler angle (ϕ=0°,θ=19.5°, Ψ=0°). The dispersion curves are as of normalizedexcitation-electrode film thickness (Hs/λ)=0 and normalized back-surfaceelectrode film thickness (Hb/λ)=0. The normalized excitation-electrodefilm thickness is defined by the wavelength λ and the thickness Hs ofthe comb-shape excitation electrode. The normalized back-surfaceelectrode film thickness is defined by the wavelength λ and thethickness Hb of the back-surface electrode.

FIG. 3 shows dispersion curves of plate waves as combinations oflongitudinal waves, fast lateral wave, slow lateral waves, andelectromagnetic waves. The horizontal axis of the graph is the productof wave number k and the plate thickness H. A plate wave is a complexcombination of the above-described waves, and there are countlessvibration modes ranging from a fast vibration mode in which the phasevelocity Vis equal to or more than 10000 m/s to a slow vibration mode inwhich the phase velocity Vis approximately 3000 m/s. In the acousticwave device disclosed in the present application, such a vibration modeis selected and used, from among the plurality of vibration modes, thatthe electromechanical coupling coefficient K² is high and apredetermined frequency temperature characteristic is satisfied. In FIG.3, a vibration mode used in the present application is indicated by asolid line, unnecessary vibration modes are indicated by broken lines.In the present application, such a vibration mode is selected that thephase velocity Vis 3500 to 4500 m/s at 5.0 to 7.5 kh indicated by thesolid line. The selected vibration mode is a vibration mode in which theelectromechanical coupling coefficient K² is highest among plate wavevibrations counted from the one with the lowest phase velocity V.Further, the selected vibration mode is the first vibration mode inwhich the figure of merit is two or more among plate wave vibrationscounted from the one with the lowest phase velocity V. In all the othervibration modes in which the phase velocity Vis lower than in theabove-described vibration mode, the electromechanical couplingcoefficient K² is as significantly small as equal to or less than 0.02%.Therefore, in a vibration mode occurring in an area of lower phasevelocity V than that of the principal vibration, the figure of meritdoes not become two or more.

FIGS. 4 to 6 are graphs of plate waves propagating in crystal substratesspecified by the Euler angle (0°, θ, 0°) and the normalized platethickness (H/λ), showing a relationship between: the frequencytemperature characteristics in the vibration mode used in the presentapplication (namely, the primary temperature coefficient α, thesecondary temperature coefficient β, and the tertiary temperaturecoefficient γ); the rotational angle θ; and H/λ. The curves shown in thegraphs indicate values calculated with θ in the range of from 16° to 21°under three conditions: H/λ is 1.63, 1.70, and 1.77. Also, Hs/λ=0.0027,and Au is used as the electrode material. As illustrated in FIG. 4, whenH/λ=1.7, a becomes a value of approximately zero in the vicinity ofθ=18.3. As illustrated in FIGS. 5 and 6, β and γ become values ofapproximately zero throughout the 0 range. Thus, it is seen that therotational angle θ has an influence only on α, and has no or minimalinfluence on β and γ.

FIGS. 7 to 9 are graphs of a relationship between the frequencytemperature characteristic (the primary temperature coefficient α, thesecondary temperature coefficient β, and the tertiary temperaturecoefficient γ) of an acoustic wave device using a crystal substratehaving a Euler angle (0°, 18.5°, 0°) is used. The relationship isobtained by calculation with H/λ changed for each Hs/λ. Hs/λ was setusing Au under five conditions: 0.0013, 0.0026, 0.0039, 0.0052, and0.0065. As illustrated in FIG. 7, a relative to Hs/λ under the fiveconditions becomes a value of approximately zero in the vicinity ofH/λ=1.65 to 1.75. As illustrated in FIG. 8, β is distributed in thevicinity of the value of zero with H/λ in the range of from 1.5 to 1.8.As illustrated in FIG. 9, γ becomes a value of approximately zero withH/λ in the range of from 1.5 to 2.0. Also in FIGS. 8 and 9, sharp riseand fall phenomena are observed in the vicinity of the lower limit andthe upper limit of H/λ. This is attributed to a combination with avibration mode adjacent to the principal vibration, causing H/λ to bechanged by Hs/λ. In a range in which such change occurs, the variationof the frequency temperature characteristic of the acoustic wave deviceat production time increases, which is not preferable from a productionpoint of view. Under the circumstances, the above-described calculationresult shows that by setting H/λ in the range of from 1.5 to 2.0relative to Hs/λ under the five conditions, a predetermined frequencytemperature characteristic is satisfied.

FIG. 10 shows one example of admittance Y characteristic in a case wherean acoustic wave device is established with: the Euler angle (0°, 19.5°,0°); H/λ=1.7; Hs/λ=0.00266; no back-surface electrode attached forfrequency adjustment anchor purposes; and 300 pairs (600) of comb-shapeexcitation electrodes attached. FIG. 11 shows a comparison of the phasevelocity V with theoretical values in a vibration mode in which awaveform of the acoustic wave device is observed. The comparison showsthat the phase velocity Vis approximately coherent, showing that asatisfactory level of analysis accuracy is obtained. Also, as clearlyseen from FIGS. 10 and 11, all the unnecessary vibrations locatedfarther in the low velocity area than the principal vibration aresignificantly small in excitation level. In the vicinity of phasevelocity V=5700 m/s, there is a mode (vibration mode 3) which is otherthan the principal vibration and in which a large waveform is observed.In this vibration mode, the electromechanical coupling coefficient Inssmaller than that of the principal vibration; the equivalent seriesresistance R1 is higher than that of the principal vibration; andfurther, the frequency is higher than that of principal vibration.Therefore, this vibration mode has no influence on an oscillation at theoscillation circuit.

FIGS. 12 to 14 show a comparison between theoretical values andexperimental values of a relationship between α, β, and γ in a casewhere an acoustic wave device is established with: Au used as theelectrode material; Hs/λ=0.00266; and no back-surface electrodeattached. The relationship is obtained with H/λ changed under fourconditions: θ=18.5, 19.5, 20.0, and 20.5. For α illustrated in FIG. 12,a value of approximately zero is observed when H/λ at four θs is about1.5. For β illustrated in FIG. 13, the curves of θ=18.5, 19.5, 20.0, and20.5 are approximately in an overlapped state, and a value ofapproximately zero is observed when H/λ is in the range of from 1.6 to1.7. Similar trends are observed in the experimental values. For γillustrated in FIG. 14, the curves of θ=18.5, 19.5, 20.0, and 20.5 areapproximately in an overlapped state, and a value of approximately zerois observed when H/λ is in the range of 1.3 to 2.0. While theexperimental values are slightly larger than the theoretical values, thedifference in value is as significantly small as 0.3×10⁻¹⁰. For each θ,β and γ change subtly, and only a can be corrected to a large degree.Thus, in order to satisfy a predetermined frequency temperaturecharacteristic, it is possible to correct the cutting angle at H/λ whereβ=0, thereby making α=0. Thus, as illustrated in FIGS. 12 to 14, bymaking θ=18.5 and H/λ=1.67, an acoustic wave device in which apredetermined frequency temperature characteristic is satisfied isobtained. It is to be noted, however, that the above-describedconditions are in the case where Au is used as the electrode materialand Hs/λ=0.00266, and that based on the electrode material and/or Hs/λ,it is necessary to make an optimal combination where α=β=0. It is to benoted that while in the experimentation Cr is used as a contact metalunder the Au electrode, since the thickness of Cr significantly small,Cr has no influence on the verification of the frequency temperaturecharacteristic. As the contact metal, it is possible to use anothermetal such as nickel (Ni), titanium (Ti), and an alloy of the foregoing.

FIGS. 15 to 17 show a comparison between theoretical values andexperimental values of a relationship between α, β, and γ in a casewhere Au is used as the electrode material and H/λ is changed withHs/λ=0.00266, 0.00532. FIGS. 15 to 17 show that relative to Hs/λ, α andβ change, while γ changes significantly subtly. Thus, as describedabove, with such H/λ that β=0 depending on Hs/λ, by correcting θ so thatα=0, it is possible to make α=β=0 while maintaining γ at a small level,ensuring that a predetermined frequency temperature characteristic issatisfied.

As has been described hereinbefore, it has been confirmed that theacoustic wave device disclosed in the present application is capable ofmaking an oscillation of a high-frequency basic wave and has a frequencytemperature characteristic equal or superior to the frequencytemperature characteristic of an AT-cut crystal resonator. Also, all theunnecessary vibrations whose phase velocity Vis lower than the phasevelocity V of the principal vibration used in the disclosure in thepresent application have an electromechanical coupling coefficient K² assignificantly small as equal to or less than 0.02. Thus, as illustratedin FIG. 10, the equivalent direct resistance R1 of the unnecessaryvibrations is significantly high, and the figure of merit is kept at orbelow two. This eliminates or minimizes oscillation errors caused byunnecessary vibrations located farther in the low frequency area thanthe main vibration, which is a problem inherent in typical Lamb waves.This eliminates the need for a frequency characteristic adjustmentcircuit (such as an LC filter circuit) in the oscillation circuit, andmakes a simple circuit sufficient, such as a typical Colpittsoscillation circuit. FIG. 18 shows an example optimal result offrequency temperature characteristic of the acoustic wave device.Production conditions are: the Euler angle (0°, 18.33°, 0°); H/λ=1.696;Hs/λ=0.0027; and Hb/λ=0.0002. The acoustic wave device produced has sucha frequency temperature characteristic that α=0.03×10⁻⁶, β=0.08×10⁻⁸,and γ=0.32×10⁻¹⁰. While in FIG. 18 the value of Hb/λ is specified as anactual production condition, it has been confirmed that in FIG. 17 andprior drawings, the above-described various conditions of the crystalsubstrate where Hb/λ=0 can be applied, such as the Euler angle (ϕ, θ,Ψ), the phase velocity V, H/λ, and Hs/λ, in which case a frequencytemperature characteristic equal to the frequency temperaturecharacteristic where Hb/λ=0 is obtained.

Also, while a reflector is omitted in FIG. 1, it is possible to obtain alarge amount of resonance without providing a reflector by setting thedimensions of the crystal substrate 12 so that a plate wave having awavelength of λ generates a standing wave at both end surfaces of thecrystal substrate 12 in its longitudinal direction, which serve asboundaries. For example, a large amount of resonance can be obtained by:as illustrated in FIG. 19A, making such a setting that the length of thecrystal substrate 12 in the X axis direction is integer N times thewavelength A; or as illustrated in FIG. 19B, decreasing the number ofone-side electrode fingers facing the other-side electrode fingers andmaking such a setting that the length of the crystal substrate 12 in theX axis direction is (N−0.5 times) the wavelength λ. The crystalsubstrate 12 is close to a Z plate, and the propagation direction of aplate wave is parallel to the X axis. With this configuration, when astanding wave is generated at both end surfaces of the crystal substrate12, which serve as boundaries, the both end surfaces become a +X surfaceand a −X surface of a quartz crystal. These surfaces are surfaces wherethe most perpendicularly stable side surfaces are formed at the time ofetching punching and thus approximately perpendicular reflectionsurfaces are formed, ensuring that a stable standing wave is generated.

The vibration mode of the plate wave disclosed in the presentapplication is a lowest frequency mode among the vibration modes havinga figure of merit in excess of two, and the Euler angle, H/λ, and Hs/λare set so that α, β, and γ become values of approximately zero. Thisensures that a typical Colpitts oscillation circuit can be used to makea stable oscillation. Also, as described above, all the unnecessaryvibrations whose phase velocity V is lower than the phase velocity V ofthe principal vibration used in the disclosure in the presentapplication have an electromechanical coupling coefficient K² assignificantly small as equal to or less than 0.02. This ensures that anexcellent frequency characteristic, with minimized phase noise andjitter, is obtained over a wide range of temperature. Generally, aninductive state is ensured insofar as the figure of merit is two ormore, and an oscillation can be made by a Colpitts oscillation circuit.If, however, the figure of merit is less than two, the reactancecomponent becomes positive, that is, an inductive state is not ensured,and an oscillation cannot be made using a Colpitts oscillation circuit.

In the process of producing the acoustic wave device 11 disclosed in thepresent application, such a condition is set that the principalvibration has a figure of merit of two or more and the unnecessaryvibration has a figure of merit of less than two. Under this condition,the thickness of the crystal substrate and the thickness of theback-surface electrode are determined. This effectively eliminates orminimizes oscillations caused by unnecessary vibrations, ensuring thatmore stable oscillation characteristics are obtained.

Also, the plate wave is in a vibration mode in which a lateral wave anda longitudinal wave are combined, and there occurs a plurality ofvibration-modes, as illustrated in FIG. 3, each corresponding to adifferent degree of combination of the lateral wave and the longitudinalwave. In these vibration modes using plate waves, as opposed toconventional Rayleigh waves, there may be other vibration modes than thenecessary principal vibration mode. Specifically, there may be vibrationmodes that are different in phase velocity and that have a highelectromechanical coupling coefficient K² (unnecessary vibrations). Whenan acoustic wave device is established so that the reflectioncoefficients of the principal vibration and an unnecessary vibrationhave the same sign, the equivalent series resistance R1 of theunnecessary vibration may in some cases be lower than the equivalentseries resistance R1 of the principal vibration mode. This has caused anabnormal oscillation at the time when an oscillation is made at anoscillation circuit.

However, as illustrated in FIG. 11, the vibration mode (S3) of the platewave selected in the acoustic wave device disclosed in the presentapplication has the highest electromechanical coupling coefficient K²among the plurality of vibration modes, and has the relationship K²>K²(X) with the electromechanical coupling coefficient K² (X) of avibration mode in which the phase velocity Vis lower than the selectedvibration mode. This eliminates or minimizes an abnormal oscillation atthe time when an oscillation is made at an oscillation circuit.

REFERENCE SIGNS LIST

-   α Primary temperature coefficient-   β Secondary temperature coefficient-   γ Tertiary temperature coefficient-   λ Wavelength-   V Phase velocity-   Y Admittance-   H/λ Normalized plate thickness-   Hs/λ Normalized excitation-electrode film thickness-   Hb/λ Normalized back-surface electrode film thickness-   11 Acoustic wave device-   12 Crystal substrate-   13 Excitation electrode-   14 Back-surface electrode-   15, 16 Comb-shape excitation electrode-   15 a, 16 a Base electrode-   15 b, 16 b Electrode finger

What is claimed is:
 1. An acoustic wave device comprising: a crystalsubstrate cut from a quartz crystal boule having three-dimensionalcrystal orientations defined by an X axis, a Y axis, and a Z axis, thequartz crystal boule being cut on the Y axis and the Z axis while beingrotated about the X axis, the quartz crystal boule being cut by arotational angle specified by a right-handed Euler angle (ϕ, θ, Ψ); andat least one comb-shape excitation electrode configured to excite thecrystal substrate to make plate waves, wherein the crystal substrate ismade by cutting the quartz crystal boule such that the rotational angleis within ranges of ϕ=0±2°, θ=17.5° to 19.5°, and Ψ±2°, wherein a platewave, among the plate waves, having a phase velocity in a range of from3500 to 4000 m/s, is selected as a vibration mode of the crystalsubstrate, and wherein when H represents a substrate-thickness of thecrystal substrate and λ represents a wavelength of the plate waves, anormalized substrate-thickness H/λ is in a range of 1.5<H/λ<2.0.
 2. Theacoustic wave device according to claim 1, further comprising: at leastone comb-shape excitation electrode configured to excite plate waves ona front surface of the crystal substrate; and a back-surface electrodeprovided on a back surface of the crystal substrate and configured toadjust frequency.
 3. The acoustic wave device according to claim 2,wherein when the comb-shape excitation electrode has a film thickness ofHs and the plate waves have the wavelength λ, a normalized filmthickness Hs/λ of the comb-shape excitation electrode is in a range of0.0013<Hs/λ<0.0065.
 4. The acoustic wave device according to claim 1,wherein the vibration mode of the selected plate wave has a lowestfrequency among a plurality of vibration modes of plate waves eachhaving a figure of merit in excess of two.
 5. The acoustic wave deviceaccording to claim 1, wherein the vibration mode of the selected platewave has a highest electromechanical coupling coefficient among aplurality of vibration modes each having a phase velocity in a range offrom 3500 to 4000 m/s, and the electromechanical coupling coefficient ishigher than an electromechanical coupling coefficient of a vibrationmode of a plate wave having a phase velocity lower than the phasevelocity of the selected vibration mode of the selected plate wave. 6.The acoustic wave device according to claim 2, wherein the comb-shapeexcitation electrode comprises a metal film comprising Au or Al as amain component.